positive solution of non-square fully fuzzy linear system of equation in general form using least square method

In this paper, we propose the least-squares method for computing the positive solution of a m × n fully fuzzy linear system (ffls) of equations, where m > n, based on kaffman’s arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coefficient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the non-square ffls of equations by using pseudoinverse. if 1-cuts vector is non-negative, we solve constrained least squares problem for computing left and right spreads. then, in the special case, we consider 0 is belong to the support of some elements of coefficient matrix and solve three overdetermined linear systems and if the solutions of these systems held in non-negative fuzzy solutions then we compute the solution of the non-square ffls of equations. else, we solve constrained least squares problem for obtaining an approximated non-negative fuzzy solution. finally, we illustrate the efficiency of the proposed method by solving some numerical examples.